The present invention relates to an apparatus for detecting an eccentricity of a roll in a rolling mill, and more particularly to an apparatus incorporating an improved detection method for detecting an eccentricity of a backup roll.
In a rolling mill for rolling steel sheets or the like, a change in roll gap caused by an eccentricity of backup rolls results in the variation in thickness of rolled sheets or the variation in tension applied to the sheets. These variations significantly hinder the improvement on the manufacture quality and disturb a stable rolling operation.
Particularly, a rolling mill provided with a roll gap controller of a quick response has recently been used. To positively use this high response quality and manufacture rolled materials having an excellent accuracy in thickness, it is essential to eliminate an eccentricity of a roll.
Generally, it is common to detect a roll eccentricity in such a way that the sum of the eccentricity quantities of upper and lower backup rolls is detected from a rolling pressure signal.
However, a rolling operation with different peripheral velocities has recently been adopted to regulate the crown or shape of a sheet, wherein the upper and lower rolls have different peripheral velocities. In this case, since the eccentricity frequency of the upper and lower backup rolls differ from each other, a substantial eccentricity may be present even if the sum of the eccentricity quantities becomes 0. Thus, to obviate such a case, it is necessary to detect the eccentricity qualities of the upper and lower backup rolls independently from each other.
In view of this, a method has been adopted heretofore as described in the following wherein only a fundamental frequency of the roll eccentricity is considered in spite of the fact that it also includes harmonics.
The sum .DELTA.S.sub.1 of the eccentricity quantities of the upper and lower backup rolls at a first measurement can be given by: EQU .DELTA.S.sub.1 =X.sub.A sin (.omega..sub.A t+.PHI..sub.A)+X.sub.B sin (.omega..sub.B t+.PHI..sub.B) (1)
Next, a second measurement is carried out under a condition that a relative phase between the upper and lower backup rolls is changed by .alpha. by rotating one of the two rolls and stopping the other. The sum .DELTA.S.sub.2 at the second measurement can be given by: EQU S.sub.2 =X.sub.A sin (.omega..sub.A t+.PHI..sub.A)+X.sub.B sin (.omega..sub.B t+.PHI..sub.B +.alpha.) (2)
The parameters used in the above two equations mean that:
X.sub.A : eccentricity of the upper backup roll, PA1 X.sub.B : eccentricity of the lower backup roll, PA1 .omega..sub.A : angular velocity of the upper backup roll, PA1 .omega..sub.B : angular velocity of the lower backup roll, PA1 .PHI..sub.A : initial phase of the upper backup roll, PA1 .PHI.B: initial phase of the lower backup roll, and PA1 .alpha.: relative lead angle between the upper and lower backup rolls.
Thereafter, the data at the first measurement is subjected to a Fourier analysis to obtain an absolute value .vertline..DELTA.S.sub.1 .vertline. and phase .epsilon..sub.1 of .DELTA.S.sub.1 of the equation (1). Similarly, the data at the second measurement is subjected to a Fourier analysis to obtain an absolute value .vertline..DELTA.S.sub.2 .vertline. and phase .epsilon..sub.2 of .DELTA.S.sub.2 of the equation (2). Consequently, each eccentricity .DELTA.S.sub.1 and .DELTA.S.sub.2 can be given by: ##EQU1##
The eccentricity quantities X.sub.A and X.sub.B and phases .PHI..sub.A and .PHI..sub.B, respectively of the upper and lower backup rolls, are solved from the equations (3) and (4). However, according to the prior art, it has been assumed that .omega..sub.A =.omega..sub.B. Therefore, each solution X.sub.A, X.sub.B, .PHI.A or .PHI..sub.B becomes: ##EQU2## where .beta. is a phase difference between .DELTA.S.sub.1 and .DELTA.S.sub.2.
As stated above, in the conventional method, it has been assumed that .omega..sub.A =.omega..sub.B in solving the eccentricity and phase.
However, in case where the diameters of the upper and lower work rolls or backup rolls differ from each other, the angular velocities in rotation of the upper and lower backup rolls generally differ from each other so that the equations (3) and (4) cannot be solved in case of different peripheral velocities. Therefore, with the conventional method, it is difficult to detect the correct eccentricity of a roll.